MHTCET 13 May 2023 Shift 2 Solved Paper

Given curve y=a√x+bx passes through (1,2).
The area formed by curve line x=4 and X-axis is 8 sq units.
∵ Since, the curves y=a√x+bx passes through (1,2).
∴‌‌2=a√1+b⋅1\a+b=2...(i)
Now, the area enclosed by the curve line x=4 and X-axis
‌=

4

∫

0

y‌dx=

4

∫

0

(a√x+bx)‌dx
‌=[a⋅‌

x 3 2

3 2

+b⋅‌

x2

2

]04
‌=‌

2a

3

⋅4‌

3

2

+‌

b

2

⋅42=‌

16a

3

+8b
From the problem
‌

16a

3

+8b=8
∴‌‌2a+3b=3...(ii)
From Eqs. (i) and (ii), we get
a=3,b=−1